On the mathematical trail of dengue: a representation of the dynamics of the flavivirus in Colombia
...
Cárdenas Avendaño, Alejandro | 2021
Infectious diseases have always been present in humans’ lives, from the flu virus to
animal-borne diseases such as dengue fever. Finding a cure for these diseases has
become the goal of many scientific investigations. Although many medical advances
have been made, even today, many diseases have no cure or treatment; this is the
case of dengue, a virus transmitted by the bite of the Aedes aegypti mosquito that
affects a large part of the world population, and in particular, in Colombia. If there
is no cure, neither a treatment for this virus, ¿which is the best way to approach it?
Mathematics! Modeling and simulating this disease allows us to study its dynamics
and ways to understand it better.
There are several studies in the literature about diseases transmitted by mosquitoes,
and perhaps the most famous is the Ross-Macdonald model, first developed to study
malaria. There are several studies on the dynamics of dengue in Colombia, specially
developed for Cali, the city with historically the highest number of dengue cases
in an outburst. This work presents a descriptive analysis of Choc´o, Huila, and
Antioquia’s departments and stability analysis and adaptation of the mathematical
model Ross-Macdonald on the dynamics in Antioquia. These departments were
chosen because the dengue virus is a public health problem, and not many studies
have been conducted on the virus in these specific territories. Simultaneously, each
of these departments provides a heterogeneous environment for the spread of the
virus, such as different socioeconomic and climatic scenarios. A Bayesian method is
used to estimate the model parameters and a Markov Chain Monte Carlo (MCMC)
simulation. To our knowledge, this work presents the first MCMC application to
the study of dengue.
The descriptive analysis determined the most vulnerable age and the influence of
gender for possible infections in each department, as well as the probability of hospitalization
for dengue and severe dengue. It is found that the Ross-Macdonald does
not apply to the recent outbreaks of dengue in the studied regions. In particular,
Choc´o has a large variability that the model cannot accurately describe; and Huila
has a periodicity over several weeks, making the model not applicable. However,
the model reasonably reproduces some parts of the outbreaks in Antioquia. The
technique used allowed for a detailed description of dengue dynamics and gave us
confidence that the fits found were robust. We conclude with some remarks and
ways to extend this analysis.
LEER
